Recognisable languages over monads [article]

Mikołaj Bojańczyk
2015 arXiv   pre-print
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of composing structures into bigger structures. It so happens that category theory has an abstract concept for this, namely a monad. The goal of this paper is to propose monads as a unifying framework for discussing existing algebras and designing new algebras.
arXiv:1502.04898v1 fatcat:2in7ckqcvje7ddulnd7nmfn5jm